A gizmodo article about the Fourier transform seemed to help with learning it a bit better. I've been trying to understand it off and on for a while now.
From that, I think I finally got that the integral is summing up an infinite series of what I'm assuming are convolutions or inner products of the different sinusoids and the signal. Assuming that is kinda like how a dot product of two vectors tells how much they have in common, but instead it is saying how much the signal has in common with the different frequencies in the new domain. Need to check on that later.
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